In the previous sections, we have introduced the novel concept of PISC plots, choosing the xSM as a concrete example to illustrate our idea.
Based on the results in Fig. REF  and REF , we are therefore now able to compare our new idea to other approaches in the literature for presenting the sensitivity of future experiments to the GW signal from a SFOPT (for a more comprehensive discussion, see Ref. [1]}).
A commonly employed strategy, e.g., is to plot the full GW spectrum together with the standard power-law-integrated sensitivity curves, which were introduced by Romano and Thrane in Ref. [2]}.
This approach conveys a useful impression of a given experiment's sensitivity reach, but comes with a number of limitations.
First of all, it requires one to draw an individual GW spectrum as a function of frequency for each parameter point of interest.
This quickly becomes impracticable, resulting in very busy plots as soon as one intends to study \(\mathcal {O}\left(10\right)\)  or more points in the model parameter space.
A possible way out of this problem would be to restrict oneself to representing each spectrum by merely a single point: a point indicating the peak amplitude at the peak frequency.
In fact, such a strategy would result in plots similar to our PISC plots.
However, the important difference in this case would be that a scatter plot of peak amplitudes and peak frequencies in combination with power-law-integrated sensitivity curves would no longer contain any information on the expected SNR.
To see this, recall that power-law-integrated sensitivity curves only have a well-defined statistical meaning for GW signals that are described by a pure power law (hence the name).
For a GW signal from a SFOPT, this assumption is maximally violated close to the most relevant part of the spectrum, namely, the peak in the spectrum, where the frequency dependence changes from a positive power law to a negative power law.
A main motivation behind our PISC approach therefore is to remedy this shortcoming.
Our PISC plots also feature observables such as GW frequencies and signal strengths on the axes; but in contrast to the standard power-law-integrated sensitivity curves, our PISCs are constructed such that they still retain the full information on the SNR.
For a given point in a PISC plot, the (partial) SNR simply corresponds to the vertical separation between the point and the PISC of interest.
We therefore argue that our PISCs are the better choice compared to the standard power-law-integrated sensitivity curves for this type of signal.
As long as the shape of the signal is not precisely known, it is reasonable to stick to power-law-integrated sensitivity curves.
However, as soon as more information on the signal shape is available, which is the case for the GW signal from a SFOPT, one should also make use of this extra information and account for it in the construction of the sensitivity curves.
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